Remark
3
[07S](Solved on 2023-01-17) Recall that the supremum \(\sup A\) of \(A⊆ X\) is (by definition) the minimum of the majorants (quando questo minimo esiste).
If \(X\) is well ordered we have the existence of the supremum \(\sup A\) for any \(A⊆ X\) that is upper bounded. 1 (If \(A\) is not upper bounded, we can conventionally decide that \(\sup A=∞\)).